Paxton, 23, allowed a one-out triple to Kyle Seager on a ball that sailed over left fielder Trayvon Robinson but struck out Brendan Ryan and Casper Wells and got Mike Carp to ground out to first in his inning.
Walker, 19, surrendered only a single to Ichiro Suzuki while inducing Chone Figgins, Dustin Ackley and Justin Smoak into groundouts.
Hultzen, 22, struck out John Jaso and Carlos Peguero before giving up singles to Luis Jimenez and Adam Moore. But he got out of his inning with a groundout by Francisco Martinez.
"I definitely calmed down a little bit," Paxton said. "Last time I had the first-time jitters a little bit. I was a lot more calm and was throwing strikes, which is the biggest thing in Spring Training."
The three will throw Monday in a "B" game before making their Cactus League debuts later next week. Walker is eager to make the next step, but had plenty to relish after facing the Mariners top of the order and giving up just the hit to Ichiro.
"You try not to think about the people in the box and the names," Walker said. "You don't want to get caught up in that. Obviously it's cool because I watched them on TV growing up, but I try to treat them like anybody else and just throw strikes. I'm just concentrating on my stuff right now, trying to pound the strike zone with my fastball and get ahead in counts."
Manager Eric Wedge said the key now is for the youngsters to just experience a big league camp and that it's too early to tell how close they are to being ready for the Majors.
"I felt they were all more comfortable out there," he said. "There's no denying their stuff, but I felt they were all more comfortable and very impressive. They pounded the zone better. It was what you want to see the second time out there after getting the first one out of the way."